Accuracy Borrowing in the Estimation of the Mean by Shrinkage to an Interval

Abstract

The topic of the shrinkage of an estimator for the mean of a normal distribution towards a point ([3] Thompson) is extended to shrinkage to an interval centered at μ = 0. An effort is made to keep the form of the modified estimator relatively simple, while obtaining more flexibility than is possessed by the sample mean . The family of estimators advocated is: Curves of MSE/σ (where MSE is mean square error) versus |μ/| are given for a number of values of θ and κ. A table is given by the use of which κ and θ may be selected on the basis of the minimum value of MSE/σ, the width of the interval for which MSE/σ < 1, the maximum value of MSE/σ, and the value of |μ/| for which MSE/σ is a maximum.